A control method for a manipulator with a disturbance observer

Abstract

The present invention relates to a manipulator control method with a disturbance observer, the method establishes a single-joint manipulator mathematical model considering disturbance; constructs a disturbance observer to obtain an estimate of the disturbance; designs a preset performance function to limit the tracking error generated by the single-joint manipulator mathematical model; combines a rate function and utilizes a nonlinear transformation to convert the restricted tracking error into an unrestricted variable; constructs a first-order filter based on the unrestricted variable and the backstepping method; designs a manipulator control law based on dynamic event triggering based on the estimate of the disturbance and the output of the first-order filter, and realizes that the tracking error converges according to the preset performance. In addition, the control method of the present invention has a simple structure, a strong anti-disturbance capability, and can effectively reduce the data transmission between the controller and the actuator.

Description

Technical Field

[0001] The invention relates to the field of mechanical arm control, and in particular to a mechanical arm control method with a disturbance observer. Background Art

[0002] Robotic arms have been widely used in defense, medical and industrial fields. Improving the trajectory tracking accuracy and dynamic performance of the robot control system is a hot topic in current research. The robot is a nonlinear mechanical system that is affected by disturbances during operation, which poses a challenge to its preset performance control. In the existing technology, when designing the preset performance controller of the robot, most of them do not construct a disturbance observer. If the disturbance increases, the trajectory tracking accuracy will decrease and the control signal will fluctuate severely.

[0003] Preset performance control is a typical method for designing a robot controller, but most of the current preset performance control methods require prior knowledge of the initial tracking error. In other words, the initial tracking error must be within a preset range to be effective, which has certain limitations. Traditional robot control methods require taking the time derivative of the virtual control law, however, this operation increases the complexity of the control method.

[0004] In the classic robotic arm sampling control system, the controller transmits the output data to the actuator in real time. If the sampling frequency is too high, a lot of communication resources will be wasted and the actuator will act frequently, thus reducing its service life. The existing event-driven method can reduce the transmission of control signals to a certain extent. How to use the dynamic event triggering method to further reduce the transmission of control signals is a problem worth studying. In summary, for a single-joint robotic arm considering disturbances, designing a control method based on dynamic event triggering without using the initial tracking error is a difficulty in the field of robotic arm control. Summary of the invention

[0005] The present invention provides a robot arm control method with a disturbance observer, which aims to solve the problems that the existing control method fails to make the robot arm trajectory tracking error converge with a preset performance without using the initial tracking error, fails to estimate the disturbance online, and wastes a lot of communication resources of the control system.

[0006] To achieve the above object, the present invention adopts the following technical solutions, including:

[0007] The control method of the manipulator with a disturbance observer includes the following steps:

[0008] Step 1. Establish a mathematical model of a single-joint robotic arm considering disturbances;

[0009] Step 2. According to the mathematical model of the single-joint robot arm, a disturbance observer is constructed to obtain the estimated value of the disturbance;

[0010] Step 3. Design a preset performance function to limit the tracking error χ1 generated by the mathematical model of the single-joint robotic arm;

[0011] Step 4. Combined with the rate function, the restricted tracking error χ1 is converted into an unrestricted variable η1 using a nonlinear transformation;

[0012] Step 5. Construct a first-order filter based on the unrestricted variable η1 and the backstepping method;

[0013] Step 6. Based on the disturbance estimate and the output of the first-order filter, design the robot control law based on dynamic event triggering to achieve the convergence of the tracking error according to the preset performance.

[0014] Furthermore, the mathematical model of the single-joint robotic arm considering disturbance described in step 1 is:

[0015]

[0016] Where q is the joint angle position, is the joint angular velocity, is the joint angular acceleration, J m is the moment of inertia of the motor, V m is the viscous friction coefficient, M m is the mass of the joint, l m is the distance from the joint axis to the center of mass, g is the acceleration due to gravity, Δ dis is the disturbance, and u is the control torque provided by the motor.

[0017] Furthermore, the disturbance observer in step 2 is:

[0018]

[0019] Among them, X z is an auxiliary variable, is an auxiliary variable, Denotes the disturbance Δ dis The estimated quantity, l d1 , l d2 and l d3 is a design parameter and is a positive number, 0<α d <1 and β d >1 is the design parameter, and α d and β d The choice should also ensure and is a real number.

[0020] Furthermore, the tracking error in step 3 is:

[0021] χ1=qqd

[0022] Among them, q d represents the desired trajectory;

[0023] The default performance functions are:

[0024]

[0025] Among them, h p and l p is a design parameter and is a positive number, ρ T is the setting time for error convergence, ρ f is the preset range for error convergence, t represents time, and π represents pi.

[0026] Furthermore, the unrestricted variable η1 in step 4 is:

[0027]

[0028] Among them, ρ p represents the preset performance function for limiting the tracking error χ1, and the variable ν e =γ s χ1,γ s is the rate function, and its expression is

[0029]

[0030] Among them, t represents time, π represents pi, γ T is the time parameter, and 0<γ T <ρ T .

[0031] Furthermore, the first-order filter in step 5 is:

[0032]

[0033] Among them, τ om >0 indicates design parameters, α xf represents the output of the first-order filter, Represents α xf The time derivative of the virtual control law α x1 The expression is:

[0034]

[0035] in, Yes d The time derivative of k1 and b1 are design parameters and are positive numbers.

[0036] Furthermore, the robotic arm control law based on dynamic event triggering in step 6 is:

[0037]

[0038] Among them, a de 、b de and ρ de is a design parameter and is a positive number, ξ de =u-α x2 , l is a positive integer, t represents time, θ de represents the intermediate variable, the virtual control law α x2 The expression is:

[0039]

[0040] Among them, k2>1 is the design parameter, is the error variable.

[0041] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0042] 1. The present invention is aimed at a single-joint manipulator considering disturbances. Under the premise of not using the initial tracking error, a manipulator control method based on dynamic event triggering is designed to make the trajectory tracking error converge with a preset performance;

[0043] 2. The present invention constructs a novel disturbance observer to obtain the estimated value of the disturbance, thereby ensuring the accuracy of trajectory tracking;

[0044] 3. The present invention designs a novel dynamic event triggering method, which can reduce data transmission and save communication resources of the control system.

[0045] Based on the above reasons, the present invention can be widely promoted in the field of robot arm control. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 This is a flow chart of the control method of the present invention;

[0047] Figure 2 This is a joint angle position trajectory tracking effect diagram of the control method of the present invention;

[0048] Figure 3 This is a comparison chart of joint angle position tracking errors using different control methods;

[0049] Figure 4 It is a control signal diagram of the control method of the present invention;

[0050] Figure 5 Control signal diagram for the disturbance-free observer method;

[0051] Figure 6 is a diagram of the estimated effects of disturbance and perturbation;

[0052] Figure 7 This is a comparison diagram of the joint angle position tracking error between the control method of the present invention and the traditional event-driven method. DETAILED DESCRIPTION

[0053] The present invention is described in more detail below with reference to the accompanying drawings.

[0054] Aiming at the single-joint robot arm trajectory tracking problem considering disturbance, the present invention constructs a disturbance observer to obtain the disturbance estimate; designs a preset performance function to limit the tracking error; combines the rate function and utilizes nonlinear transformation to convert the restricted tracking error into an unrestricted variable; constructs a first-order filter based on the unrestricted variable and the backstepping method; designs a robot arm control law based on dynamic event triggering according to the disturbance estimate and the output of the first-order filter, so as to achieve the convergence of the tracking error according to the preset performance.

[0055] like Figure 1 As shown, the present invention provides a method for controlling a robotic arm with a disturbance observer, comprising the following steps:

[0056] Step 1. Establish a mathematical model of a single-joint robotic arm considering disturbances;

[0057] The mathematical model of the single-joint robotic arm considering disturbance is established as follows:

[0058]

[0059] Where q is the joint angle position, is the joint angular velocity, is the joint angular acceleration, J m is the moment of inertia of the motor, V m is the viscous friction coefficient, M m is the mass of the joint, l m is the distance from the joint axis to the center of mass, g is the acceleration due to gravity, Δ dis is the disturbance, and u is the control torque provided by the motor.

[0060] Step 2. According to the mathematical model of the single-joint robot arm, a disturbance observer is constructed to obtain the estimated value of the disturbance;

[0061] The disturbance observer is:

[0062]

[0063] Among them, X z is an auxiliary variable, is an auxiliary variable, Denotes the disturbance Δ dis The estimated value, ld1 , l d2 and l d3 is a design parameter and is a positive number, 0<α d <1 and β d >1 is the design parameter, and α d and β d The choice should also ensure and is a real number.

[0064] Step 3. Design a preset performance function to limit the tracking error χ1 generated by the mathematical model of the single-joint robotic arm;

[0065] The tracking error is:

[0066] χ1=qq d

[0067] Among them, q d represents the desired trajectory;

[0068] The default performance functions are:

[0069]

[0070] Among them, h p and l p is a design parameter and is a positive number, ρ T is the setting time for error convergence, ρ f is the preset range for error convergence, t represents time, and π represents pi.

[0071] Step 4. Combined with the rate function, the restricted tracking error χ1 is converted into an unrestricted variable η1 using a nonlinear transformation;

[0072] The unrestricted variable η1 is:

[0073]

[0074] Among them, ρ p represents the preset performance function for limiting the tracking error χ1, and the variable ν e =γ s χ1,γ s is the rate function, and its expression is

[0075]

[0076] Among them, t represents time, π represents pi, γ T is the time parameter, and 0<γ T <ρ T .

[0077] Step 5. Construct a first-order filter based on the unrestricted variable η1 and the backstepping method;

[0078] The first-order filter is:

[0079]

[0080] Among them, τ om >0 indicates design parameters, α xf represents the output of the first-order filter, Represents α xf The time derivative of the virtual control law α x1 The expression is:

[0081]

[0082] in, Yes d The time derivative of k1 and b1 are design parameters and are positive numbers.

[0083] Step 6. Based on the disturbance estimate and the output of the first-order filter, design the robot control law based on dynamic event triggering to achieve the convergence of the tracking error according to the preset performance.

[0084] The control law of the robot arm based on dynamic event triggering is:

[0085]

[0086] Among them, a de 、b de and ρ de is a design parameter and is a positive number, ξ de =u-α x2 , l is a positive integer, t represents time, θ de represents the intermediate variable, the virtual control law α x2 The expression is:

[0087]

[0088] Among them, k2>1 is the design parameter, is the error variable.

[0089] The designed robot arm control method with disturbance observer is simulated in a virtual environment to verify the feasibility of the proposed method. In the simulation experiment, the mathematical model of the robot arm is:

[0090]

[0091] Where q is the joint angle position, is the joint angular velocity, is the joint angular acceleration, J m is the moment of inertia of the motor, V m is the viscous friction coefficient, M m is the mass of the joint, l m is the distance from the joint axis to the center of mass, g is the acceleration due to gravity, Δ dis is the disturbance, and u is the control torque provided by the motor. The model parameters of the robot arm are: J m =1kg·m 2 , V m =1Nm·s / rad, M m gl m =10Nm,Δ dis =2.5sin(2πt)+4sin(3πt), the time is set to 10 seconds.

[0092] The initial state of the robot arm is q(0)=8rad, The desired trajectory is set to q d =cos(t).

[0093] The control law related parameters are set as τ om =0.01, k1=1, k2=11, b1=0.02, γ T =1,ρ T =3,h p =1,l p =1 / 6,ρ f =0.1, a de =0.1, b de =1.5,ρ de =0.1,α xf The initial value α xf (0) = -23.9264, the disturbance observer related parameters are set to l d1 =50, l d2 =2, l d3 =2,α d =3 / 7, β d =5 / 3,X z The initial value of X z (0 ) =0,θ de The initial value of θ de (0)=0.

[0094] To further illustrate the superiority of the control method of the present invention, a comparative experiment is conducted with the disturbance-free observer method and the traditional event-driven method. If it is set to 0, it is a disturbance-free observer method. The event triggering strategy adopted by the traditional event-driven method is:

[0095]

[0096] Among them, the virtual control law α x2 Same as the present invention, a cte =1.5,ξ de =u-α x2 , is a positive integer, and t represents time.

[0097] Figure 2 This is a diagram showing the effect of tracking the trajectory of the joint angle position of the control method of the present invention. It can be seen from the diagram that the control method of the present invention can achieve trajectory tracking of the joint angle position within 3 seconds.

[0098] Figure 3 The figure shows the comparison of joint angle position tracking errors using different control methods. It can be seen from the figure that although the initial tracking error is not within the preset range, the control method of the present invention can ensure that the tracking error converges with the preset performance. In addition, if there is no disturbance observer, the tracking error fluctuates greatly, that is, the tracking accuracy of the method without disturbance observer is poor.

[0099] Figure 4 This is a control signal diagram of the control method of the present invention. It can be seen from the diagram that the control signal is a piecewise constant, which effectively reduces data transmission and saves communication resources of the control system.

[0100] Figure 5 This is the control signal diagram of the method without disturbance observer. It can be seen from the figure that if there is no disturbance observer, the control signal will fluctuate, which is not conducive to the practical application of the control method.

[0101] Figure 6 is a diagram of disturbance and disturbance estimation effect. It can be seen from the figure that the disturbance observer constructed in the present invention can effectively realize the estimation of disturbance, thereby ensuring the tracking accuracy and avoiding fluctuation of the control signal.

[0102] In the experiment, the control method of the present invention has 152 event triggering times, while the traditional event-driven method has 193 event triggering times. Figure 7 This is a comparison diagram of the joint angle position tracking error of the control method of the present invention and the traditional event-driven method. It can be seen from the figure that the tracking error curves of the two methods are almost overlapped. Therefore, it can be concluded that the control method of the present invention only needs less data transmission to ensure that the tracking error converges with the preset performance.

[0103] The above simulation experiment results show that the present invention achieves the convergence of tracking error with preset performance for a single-joint manipulator considering disturbance without using the initial tracking error, and the constructed disturbance observer can effectively estimate the disturbance. In addition, the control method of the present invention has a simple structure and can effectively reduce the data transmission between the controller and the actuator.

[0104] It can be understood that the above specific description of the present invention is only used to illustrate the present invention and is not limited to the technical solutions described in the embodiments of the present invention. Those skilled in the art should understand that the present invention can still be modified or replaced by equivalents to achieve the same technical effects; as long as the use requirements are met, they are within the protection scope of the present invention.

Claims

1. A method for controlling a robotic arm with a disturbance observer, characterized in that: The steps include: Step 1. Establish a mathematical model of a single-joint robotic arm considering disturbances; Step 2. According to the mathematical model of the single-joint robot arm, a disturbance observer is constructed to obtain the estimated value of the disturbance; Step 3. Design a preset performance function to limit the tracking error χ1 generated by the mathematical model of the single-joint robotic arm; Step 4. Combined with the rate function, the restricted tracking error χ1 is converted into an unrestricted variable η1 using a nonlinear transformation; Step 5. Construct a first-order filter based on the unrestricted variable η1 and the backstepping method; Step 6. According to the disturbance estimate and the output of the first-order filter, a robot control law based on dynamic event triggering is designed to achieve tracking error convergence according to the preset performance; The mathematical model of the single-joint robotic arm considering disturbance in step 1 is: Where q is the joint angle position, is the joint angular velocity, is the joint angular acceleration, J m is the moment of inertia of the motor, V m is the viscous friction coefficient, M m is the mass of the joint, l m is the distance from the joint axis to the center of mass, g is the acceleration due to gravity, Δ dis is the disturbance, u is the control torque provided by the motor; The disturbance observer in step 2 is: Among them, X z is an auxiliary variable, is an auxiliary variable, Denotes the disturbance Δ dis The estimated quantity, l d1 , l d2 and l d3 is a design parameter and is a positive number, 0<α d <1 and β d >1 is the design parameter, and α d and β d The choice should also ensure and is a real number.

2. The method for controlling a robotic arm with a disturbance observer according to claim 1, characterized in that: The tracking error in step 3 is: χ1=q-q d Among them, q d represents the desired trajectory, q is the joint angle position; The default performance functions are: Among them, h p and l p is a design parameter and is a positive number, ρ T is the setting time for error convergence, ρ f is the preset range for error convergence, t represents time, and π represents pi.

3. The method for controlling a robotic arm with a disturbance observer according to claim 1, characterized in that: The unrestricted variable η1 in step 4 is: Among them, ρ p represents the preset performance function for limiting the tracking error χ1, and the variable ν e =γ s χ1,γ s is the rate function, and its expression is Among them, t represents time, π represents pi, γ T is the time parameter, and 0<γ T <ρ T , ρ T Set time for error convergence.

4. The method for controlling a manipulator with a disturbance observer according to claim 3, characterized in that: The first-order filter in step 5 is: Among them, τ om >0 indicates design parameters, α xf represents the output of the first-order filter, Represents α xf The time derivative of the virtual control law α x1 The expression is: in, Yes d The time derivative of d represents the expected trajectory, k1 and b1 are design parameters and are positive numbers.

5. The method for controlling a robotic arm with a disturbance observer according to claim 4, characterized in that: The control law of the robot arm based on dynamic event triggering in step 6 is: Among them, a de , b de and ρ de is a design parameter and is a positive number, ξ de =u-α x2 , u is the control torque provided by the motor, is a positive integer, θ de represents the intermediate variable, t represents time, and the virtual control law α x2 The expression is: Among them, k2>1 is the design parameter, is the error variable, η1 is an unrestricted variable, γ s is the rate function, is the joint angular velocity, V m is the viscous friction coefficient, M m is the mass of the joint, l m is the distance from the joint axis to the center of mass, g is the acceleration due to gravity, J m is the moment of inertia of the motor, q is the joint angle position, Denotes the disturbance Δ dis The estimated amount.

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